Lesson Guide
Explanation
A spinner does not remember what it did last time. If the first spin landed on blue, blue is still one out of four on the next spin — not less likely because it has just come up, and not more likely because it is on a run. The same goes for coins and dice: after three heads in a row, the next toss is still an even chance. Nothing about the object changed between goes, so nothing about the chances changed.
Your Turn
A coin has landed heads three times. What is the chance of heads next? Check: still a half.
Watch Out
"It is due" and "it is on a run" are both wrong. Each spin is independent of the last.
Explanation
A bag is different from a spinner, because taking a counter out and keeping it really does change what is left. Three red of eight becomes two red of seven: one fewer red, and one fewer counter altogether, so both numbers change. If instead the counter is put back, nothing has changed and the chance is three out of eight again. The word replaced, or kept, decides the whole question.
Your Turn
A bag has 3 red of 8. One red is taken and kept. What is the chance of red now? Check: 2 out of 7.
Watch Out
Both numbers change, not just the top one. 3 of 8 becomes 2 of 7, not 2 of 8.
Explanation
Two words that look similar mean different things. Most likely compares the outcomes with each other, so on a spinner where blue covers half and red and green a quarter each, blue is most likely. But likely compares one outcome with a half, and blue is exactly a half, so blue is an even chance rather than likely. An outcome can be the most likely and still not be likely, which is exactly the distinction these claim questions test.
Your Turn
Blue covers half a spinner. Is blue likely? Check: no — it is an even chance.
Watch Out
"Most likely" and "likely" are different tests. Check which word the claim uses.
Explanation
Here is the routine on a real set. A bag holds four red, three blue and three green, ten counters. Red is the most likely colour, because four beats three and three. But red is not likely, because four out of ten is less than a half. And blue and green are equally likely, three out of ten each. Marked one at a time that gives tick, cross, tick, so the answer is one and three — and the false statement is the one that follows naturally from the true one.
Your Turn
Is 4 out of 10 likely? Check: no — it is less than a half.
Watch Out
Being the biggest does not make something likely. Compare it with a half separately.
Explanation
Three ideas cover every claim in this chapter. A spinner, coin or die has no memory, so the last result changes nothing. A counter taken from a bag and kept changes both numbers, while one put back changes nothing. And most likely is not the same as likely. Test each statement against the numbers rather than against how sensible it sounds. Quiz and exercises now.
Your Turn
A die has shown 6 twice in a row. What is the chance of a 6 next? Check: still 1 out of 6.
Watch Out
Check whether the question is about the NEXT go or about the ones already done.
📌 Key Points — this lesson in a nutshell
- A spinner, a coin and a die have no memory. What happened last time does not change the next go.
- Taking a counter and keeping it does change the next chance, because the bag now holds fewer counters.
- "Most likely" compares the outcomes with each other. "Likely" compares one outcome with a half.
- Test each statement against the numbers, one at a time — the convincing-sounding one is often the false one.
Step 1: Introduction
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